Sorry but the very phrase "After accounting for all variables" when doing statistical analysis on any complex real-life scenario is laughable. We don't even know all the variables, much less have rigorous data for them all.

I think their theory is probably right. It makes a lot of sense and the data we do have does fit. But this is statistics, not science; correlation, not proof of causation. It is far from being without value, but it is also far from being conclusive or thorough. It is merely as thorough as it could be given available data.

That this is even a concern is just further evidence that income taxes are an affront to sane governance. Tax your bartering, hobbies, garage sales, office perks, etc, etc. It's insane, impossible to enforce, and massively burdensome.
Funding government should not be this complicated. They should stick to things that are largely enforceable and/or have direct correlation to government services:
- paperwork fees (to comp licenses, permits, patents, etc)
- tariffs (to comp border security, trade depts)
- corporate income taxes (to comp artificial, govt-provided existence)
- sin taxes (to comp societal costs of jails, child services, health care, etc that are burdened by risky consumption)
- property taxes (to comp infrastructure, police, fire, etc)
Even sales taxes make far, far more sense than income taxes. They are much easier to enforce (fewer businesses than individuals) and encourage investment over consumption (good for economy and environment). And they are easier to make non-regressive than income tax (flat rebate for everyone and/or excluding groceries). Income taxes are the most prone to complication and thus loopholes. They are the most expensive to enforce and to comply with. They get nothing from tourists, who still cost the system, and also manage to complicate immigration policy (or at least the debate around it).
Income tax is regressive, oppressive, and costly.